Abstract
Starting from simple observations regarding heat flows for static black holes (or any thermodynamic system with [Formula: see text]), we get inequalities which restrict their change in energy and adiabatic curves in the [Formula: see text] plane. From these observations, we then derive an exact efficiency formula for virtually any holographic heat engine defined by a cycle in the [Formula: see text] plane, whose working substance is a static black hole. Moreover, we get an upper bound for its efficiency and show that for a certain class of black holes, this bound is universal and achieved by an “ideal gas” hole. Finally, we compute exact efficiencies for some particular and new engines.
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